I started all 3 bodies on the x axis with the earth at the left of the system's centre of mass (COM) and the moon at the right. the rocket is between the earth and moon and therefore lies to the right of the COM and all travel anti-clockwise.

I devised the initial velocity of the rocket using v=sqrt(G*mass of earth/radius of rocket) but it's just occured to me that it maybe should have been adjusted slightly as the earth has a small rotation in the same direction as the rocket around the system's COM.

Should the earth's angular velocity be added (or taken away) from the initial velocity of the rocket in orbit? and does the moon affect the initial velocity?

It's been puzzling me all day so any comments would be appreciated!